Measurable Riemannian structures associated with strong local Dirichlet forms

Abstract

We introduce Riemannian-like structures associated with strong local Dirichlet forms on general state spaces. Such structures justify the principle that the pointwise index of the Dirichlet form represents the effective dimension of the virtual tangent space at each point. The concept of differentiations of functions is studied, and an application to stochastic analysis is presented.

14 pages

References in corpus (1)

• Martingale dimensions for fractals

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